Applications of the new scattering formalism: The Dirichlet boundary condition

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Abstract
This is the third in a series of articles concerning the theory of scattering from a rough surface. Consideration of the scattering problem for a scalar wave obeying Dirichlet boundary conditions enables one to investigate the formalism developed in the previous work. The advantages of this new representation of the scattering amplitude is discussed. This result is supplemented with an improved integral equation for the desired solutions on the surface. This new equation not only allows one to reproduce the approximations for the scattering amplitude obtained previously, but it can also be used to extend those results to higher orders. This is illustrated with a derivation of the second-Born approximation. The correction to the scattering amplitude due to a distribution of point scatters is also obtained. To the order under consideration, this phenomenon is shown to be equivalent to a perturbation of the surface. A similar result is found when the index of refraction is allowed to vary near the scattering surface.

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